Noise-induced tracking errors in discrete-time sliding mode controls for sensors

The objective of this paper is to analyze, using Itô diffusions, the stochastic non-zero-mean drifts generated by noise at the input of the comparator in first-order sigma-delta modulators implementing discrete-time sliding-mode controls. These controls have been used in constant temperature anemometry in three missions to Mars. The objective is to expand previous results obtained with discrete-time Markov chains, by using the high-rate (continuous-time) diffusion limit with Itô diffusions. The studied examples are time-variant thermal models used for the wind sensors. The distributions will be analyzed using the gradient flow interpretation, and by solving the Fokker-Planck equations. Second order stability is analyzed using the dead zone Lyapunov function analysis, for one-dimensional and multi-dimensional models. Guidelines for the design of sensors working under quasi-constant state operation are provided.